Example 4.  Use Picard iteration to find and plot approximations for the  solution of the I.V.P.  

        [Graphics:Images/PicardIterationMod_gr_62.gif].  

Solution 4.

[Graphics:../Images/PicardIterationMod_gr_63.gif]

[Graphics:../Images/PicardIterationMod_gr_64.gif]

Picard iteration for generating the first six approximations is started with the Mathematica command:

[Graphics:../Images/PicardIterationMod_gr_65.gif]

[Graphics:../Images/PicardIterationMod_gr_66.gif]

 

We can graph the analytic solution and the Picard iterations.

[Graphics:../Images/PicardIterationMod_gr_67.gif]


[Graphics:../Images/PicardIterationMod_gr_68.gif]

[Graphics:../Images/PicardIterationMod_gr_69.gif]

 

 

 

[Graphics:../Images/PicardIterationMod_gr_70.gif]


[Graphics:../Images/PicardIterationMod_gr_71.gif]

[Graphics:../Images/PicardIterationMod_gr_72.gif]

 

 

 

[Graphics:../Images/PicardIterationMod_gr_73.gif]


[Graphics:../Images/PicardIterationMod_gr_74.gif]

[Graphics:../Images/PicardIterationMod_gr_75.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005